Question: A distributor receives a new shipment of 20 iPods. He draws a random sample of five iPods and thoroughly inspects the click wheel of each of them. Suppose that the shipment contains three iPods with a malfunctioning click wheel. Let X denote the number of iPods with a defective click wheel in the sample of five.
(a) The random variable X is (choose one)
(i) binomial
(ii) hypergeometric
(iii) negative binomial
(iv) Poisson.
(b) Give the sample space and the formula for the PMF of X.
(c) Compute P(X = 1).
(d) Find the expected value and variance of X.